The antagonist entertains a person's Jungian Shadow, a fundamental aspect of their psychology.

The Jungian Shadow is a proposal by Jung, that every human has within them a dangerous alter ego that exists in their subconscious. Either you can externalize the Shadow or entertain its ideals by engaging in socially acceptable forms (such as listening to death metal or painting images that could be interpreted as disturbing), or you can repress the Shadow until it manifests itself in violent ways. This is a good reason why people such as Orthodox Christians who absolutely refuse to believe that they have a dark side often end up performing the most mentally deranged or horrifying crimes out of anyone.

Ironically, the Joker (the one in the debate thumbnail), is one very good example of a villain who is far more important to the viewer than the hero ever could be. On a subconscious level, people will always identify with the Joker's nihilism and "The only sensible way to live is without rules" philosophizing. Instead of providing cheap explosion effects, or slapping a thin veil of righteousness on the entire movie by making the villain ridiculous, villains like the Joker appeal directly to every person's dark side. That is why movie villains are very often far more important than their heroes.

The saying "A hero is only as good as its villain" is a complete understatement, as, in the end, the hero is inconsequential compared to the villain.

What if the antagonist is not a single character?

While I agree that there are many cases where the antagonist is more important than the protagonist, this black and white dichotomy doesn't account for movies where there is no central antagonist, and instead the antagonist is an ideal or a part of society. Antiheroes also do not fit into this question well.